I'm English so the notion of the death penalty is slightly disturbing in many ways as it's alien in my culture. If you have a death penalty in your society I suppose you must accept that there will be a margin of error and innocent people will die as a result of your system.
So, to follow the logical argument, and to say that's accepted, why wait so very, very long to kill your prisoners? If the system is accepted then executions should be immediately after the appeals process is complete I'd have thought.
The fact that prisoners are on death row for years suggests an underlying uncertainty in the use of the death penalty as a punishment, be that for cultural or political reasons.
The end result seems to me to be a pretty miserable torture whereby you're sentenced to several years of psychological abuse before being killed. Perhaps that's the point. Whether that's a sucessful deterrent I don't know.